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Proof step 23 from proof ushort-band-01 (previous step)

j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, abs(j0) < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ 0 ≤ j1 ∧ j0 < j ∧ j1 < j → (i * j + j0 = i0 * j + j1 ↔ i = i0 ∧ j0 = j1)
Proof step 25:
¬(0 ≤ i ∧ 0 ≤ i0 + 255 ∧ 0 ≤ j ∧ 0 ≤ 255 + j0 ∧ j < 256 ∧ 255 + j0 < 256), j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, abs(j0) < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 ≤ j0 ∧ 0 ≤ j1 ∧ j0 < j ∧ j1 < j → (i * j + j0 = i0 * j + j1 ↔ i = i0 ∧ j0 = j1) subst: [j1, i0, j0, j, i] → [255 + j0, i0 + 255, j, 256, i] rotate: F spec: int-mult inst: name: mods-eq

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0; Used terms: 255 + j0, i0 + 255, j, 256, i